Question

hlal can Joe expect at retirement? le course of his career 3.58 Find the value of X so that the two cash flows shown in the diagram are equivalent for an interest rate of 8%. A $200 $200 $200 $200 sıso $1 2. 3 4 Years 2 4 $200 ×+ $200 Years F. Rosti, Ph.D., P.E

Answer 1

Case 1

Refer to the cash diagram 1

We will refer the following formulas in this exercise.

P(P/F,i,n)= (1+i)^-n

(P/F,8%,4)=(1+8%)^-4= 0.735030

Present worth of cash flows=P1=200(P/A,8%,5)-50(P/F,8%,4)=200*3.992710-50*0.735030=761.79

P1=$761.79

Case 2

Refer to the cash diagram 2

Present worth of cash flows=X(P/A,8%,5)-(X+200) (P/F,8%,3)- (X+200) (P/F,8%,4)

(P/A,8%,5)=3.992710 (already calculated in first case)

(P/F,8%,3)=(1+8%)^-3= 0.793832

(P/F,8%,4)= 0.735030 (already calculated in first case)

Present worth of cash flows=P2=X(P/A,8%,5)-(X+200) (P/F,8%,3)- (X+200) (P/F,8%,4)

P2=X*3.992710-(X+200)*0.793832-(X+200)*0.735030

P2=3.992710X-0.793832X-158.7664-0.735030X-147.006

P2=2.463848X-305.7724

Set P1=P2

761.79=2.463848X-305.7724

X=(761.79+305.7724)/2.463848=$433.29

X should be $433.29